Abstract

In ultra-pure material non-local phenomena occur, which are not fully explained yet. Until recently, experimental measurements in graphene were limited to macroscopic properties such as the non-local resistance to describe hydrodynamic electron flow, which allows other explanations. Recent experiments describe two imaging techniques allowing to measure the charge flow directly. We show that the hydrodynamic charge flow in a finite Hall-bar shows a complex vortex pattern accompanied by an alternating non-local resistance. Our results allow to characterize electron hydrodynamics by its unique flow pattern. Further on, we show that for a compensated two-carrier system within a magnetic field, one finds a giant non-locality matching current experiments. This allows to predict the results of future experiments as well as to design further applications.